On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle

Abstract

Formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented. The general linear variation of the source is represented in terms of three linear basis functions, each one associated with a different vertex of the triangular domain. The singular kernels considered are given by the 3-D Green's function and its gradient, both for the static and dynamic case. In the static case the evaluation of potentials is performed analytically and compact form results are given. In the dynamic case the results are given in a form suited for numerical integration.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>